Given a graph G with vertex set V (G)={v1, v2,..., vn}, we associate to G a path matrix P
whose (i, j)-entry is the maximum number of vertex disjoint paths between the vertices vi and …

We prove two dichotomy results for detecting long paths as patterns in a given graph. The
NP-hard problem Longest Induced Path is to determine the longest induced path in a graph …

Abstract The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of
size at most k that induces a connected subgraph of G. This is a well-studied problem …

We prove that for every graph H, there exists a polynomial-time algorithm deciding if a
planar graph can be contracted to H. We introduce contractions and topological minors of …

Structural properties of graphs and networks have been investigated across scientific
disciplines ranging from mathematics to structural chemistry. Structural branching, cyclicity …

Sphere-bases are constructed for the ℤ 2 vector space formed by the k-dimensional
subcomplexes, of n-simplex (or n-cube), for which every (k− 1)-face is contained in a positive …

Testing if a given graph G contains the k-vertex path P k as a minor or as an induced minor
is trivial for every fixed integer k≥ 1. However, the situation changes for the problem of …

For an efficient force method of frame analysis, the formation of localized self‐equilibrating
systems is an important issue. Such systems can be constructed on minimal cycle basis of …

A construction for a minimum cycle basis for the Cartesian and the strong product of two
graphs from the minimum length cycle bases of the factors is presented. Furthermore, we …

The Path Contraction and Cycle Contraction problems take as input an undirected graph $ G
$ with $ n $ vertices, $ m $ edges and an integer $ k $ and determine whether one can …